Analytic expressions for the partial waves of the off-shell two body coulomb T-matrix

Closed form expressions for all partial waves of the pure Coulomb off-shell T-matrix p¦ T_c,l.(k ²) ¦p are obtained. All singularities appear through simple special functions, which makes it possible to study the analytic properties of p¦ T_c,l(k²) ¦p as a function not only of one of the momentap, p but even of both of them. With use of the renormalization procedure found by Zorbas the transition to half-and on-shell values is performed reproducing known expressions. By the same method simple expressions for the partial waves of the Coulomb wave function in the momentum representation are found.     

Excited states of100Tc from100Mo(p,nγ)100Tc reaction and the parabolic rule

γ-spectra and excitation functions of the¹⁰⁰Mo(p, nγ)¹⁰⁰Tc reaction were measured in the 1.2–3.6 MeV proton energy range by using thick, enriched targets, Ge(Li) and low energy photon (hyperpure Ge) spectrometers. These detectors were used inγγ-coincidence experiments, too. Conversion electron spectrum measurements were performed by means of a superconducting magnet transporter Si(Li) spectrometer (SMS) atE _p =4 MeV and multipolarities of some transitions have been determined. Based on the experimental results a level scheme of¹⁰⁰Tc has been constructed. Level energies of¹⁰⁰Tc were calculated on the basis of the parabolic rule, derived from the cluster-vibration model.     

Computational experience with known variable metric updates

Variable metric methods from the Broyden family are well known and commonly used for unconstrained minimization. These methods have good theoretical and practical convergence properties which depend on a selection of free parameters. We demonstrate, using extensive computational experiments, the influence of both the Biggs stabilization parameter and Oren scaling parameter on 12 individual variable metric updates, two of which are new. This paper focuses on a class of variable metric updates belonging to the so-called preconvex part of the Broyden family. These methods outperform the more familiar BFGS method. We also experimentally demonstrate the efficiency of the controlled scaling strategy for problems of sufficient size and sparsity.     

Algorithms for ham-sandwich cuts

Given disjoint setsP ₁,P ₂, ...,P _d inR ^d withn points in total, ahamsandwich cut is a hyperplane that simultaneously bisects theP _i . We present algorithms for finding ham-sandwich cuts in every dimensiond>1. Whend=2, the algorithm is optimal, having complexityO(n). For dimensiond>2, the bound on the running time is proportional to the worst-case time needed for constructing a level in an arrangement ofn hyperplanes in dimensiond−1. This, in turn, is related to the number ofk-sets inR ^d−1 . With the current estimates, we get complexity close toO(n ^3/2 ) ford=3, roughlyO(n ^8/3 ) ford=4, andO(n ^d−1−a(d) ) for somea(d)>0 (going to zero asd increases) for largerd. We also give a linear-time algorithm for ham-sandwich cuts inR ³ when the three sets are suitably separated. A preliminary version of the results of this paper appeared in [16] and [17]. Part of this research by J. Matoušek was done while he was visiting the School of Mathematics, Georgia Institute of Technology, Atlanta, and part of his work on this paper was supported by a Humboldt Research Fellowship. W. Steiger expresses gratitude to the NSF DIMACS Center at Rutgers, and his research was supported in part by NSF Grants CCR-8902522 and CCR-9111491.     

Spectra of unicyclic graphs

Unicyclic graphs are discussed in the context of graph orderings related to eigenvalues. Several theorems involving lexicographical ordering by spectral moments as well as the ordering by the largest eigenvalue are proved. An appendix contains a table of the 89 unicyclic graphs on eight vertices together with their spectra, spectral moments and characteristic polynomials.Carnegie Research Fellow, University of Stirling, 1985–86.     

Bull-free Berge graphs are perfect

Abull is the (self-complementary) graph with verticesa, b, c, d, e and edgesab, ac, bc, bd, ce; a graphG is calledBerge if neitherG not its complement contains a chordless cycle whose length is odd and at least five. We prove that bull-free Berge graphs are perfect; a part of our argument relies on a new property of minimal imperfect graphs.This work was done while both authors were at the School of Computer Science, McGill University; support by NSERC is gratefully acknowledged.     

Kinetics of the photodissociation iodine laser with slow pumping

Systematic calculations of maximum inversion were performed for iodine photodissociation laser in dependence on the mixture composition. The flash-lamp radiation was modelled as emanating from an optically thin Xe plasma. Duration of the pumping pulse is about 300 s. The sensitivity of the model to the values of kinetic constants was also tested.     

Laser properties of coactivated YAP: Nd free of colour centres

YAP:Nd, Cr grown under Ar-H₂ or Ar-He-H₂ atmosphere possesses good energy transfer from Cr³⁺ to Nd³⁺ but suffers from the colour centre formation. The centre formation was completely prevented using further admixture of Ce³⁺ and 10^–4–10^–3 wt. % Fe. Small luminescence quenching of Cr³⁺ or Nd³⁺ due to iron ions is negligible in the presence of Ce³⁺. The crystals may be also heavily doped with Nd³⁺ because the increased pumping efficiency compensates the shortening of the luminescence lifetime. YAP: Nd, Ce, Cr, Fe is advisible active laser material particularly for all the types of pulsed lasers.